The intuition behind \({\mathsf {UGT}}\)  (resp. \({\mathsf {IGT}}\) ) can be interpreted as the averaged attractive spring-like forces between the target user and other group members (resp. among other group members), if the source neighborhood of the target user is abstracted as a force system. This abstraction is widely adopted in graph drawing [1]}, [2]}.
Take Figure REF (a) as an example. The source neighborhood of \(v_1\)  is represented as a spring network where each edge is assumed as a spring, then the tie strength \(w_{i,j}\)  can be regarded as the stiffness constant (i.e., physical strength) of the spring on \((v_i,v_j)\in \mathcal {E} \) .
Let \(l_{i,j}\in [0,1]\)  be the natural length (when no force is exerted) of a given spring on \((v_i,v_j)\) , which is equivalent to the theoretical distance between \(v_i\)  and \(v_j\)  on the graph, as clarified in [2]}. Suppose that all springs are set to initial length 1, then the similarity \(\delta _{i,j}=1-l_{i,j}\)  indicates the displacement of the spring on \((v_i,v_j)\) .
According to Hooke's law, as shown in Figure REF (b), \(w_{i,j}\cdot \delta _{i,j}\)  is equal to the attractive force exerted by \((v_i,v_j)\) .
In contrast, group-level competitors in Section REF  only consider the tie strength [4]}, [5]}, [6]} or the in-group connectivity by the edge density [7]}, [8]}, whereas the homogeneity of group members is ignored.
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